Question

A farmer plants 7 1/5acres of green apples in his orchard. This makes up 3/8 of his entire orchard. How many acres make up the farmer's orchard?

Answer 1

The area, in acres, used to plant the green apples is

`7(1)/(5)=7+(1)/(5)=(5\cdot7+1)/(5)=(35+1)/(5)=(36)/(5)`

And this area corresponds to 3/8 of the entire orchard.

So, calling x the area of the entire orchard, we have the following proportion:

Area in acres Fraction of the orchard

36/5 3/8

x 1

Then, cross multiplying the above values, we obtain:

`\begin{gathered} (3)/(8)x=(36)/(5) \\ \\ (8)/(3)\cdot(3)/(8)x=(8)/(3)\cdot(36)/(5) \\ \\ x=(8)/(5)\cdot(36)/(3) \\ \\ x=(8)/(5)\cdot12 \\ \\ x=(96)/(5) \\ \\ x=(95)/(5)+(1)/(5) \\ \\ x=19(1)/(5) \end{gathered}`

Therefore, the area of the framer's orchard is 19 1/5 acres.